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Parikh vectors
8OHJ_1 1ZPL_1 7JSI_1 Letter Amino acid
1 2 6 C Cysteine
18 4 38 E Glutamic acid
16 8 28 I Isoleucine
14 12 37 L Leucine
0 4 14 W Tryptophan
8 17 41 V Valine
9 23 36 S Serine
16 8 40 A Alanine
6 8 25 R Arginine
7 13 27 N Asparagine
5 8 29 D Aspartic acid
2 5 27 Q Glutamine
11 20 29 G Glycine
4 4 11 M Methionine
12 14 32 T Threonine
3 7 15 Y Tyrosine
3 6 23 F Phenylalanine
3 2 11 H Histidine
9 6 40 K Lycine
7 6 27 P Proline 

8OHJ_1|Chains A, B|Cyclic di-AMP synthase CdaA|Bacillus subtilis subsp. subtilis str. 168 (224308)
>1ZPL_1|Chains A, B|F17a-G|Escherichia coli (562)
>7JSI_1|Chains A, B, C, D, E, F|Protein Rep68|Adeno-associated virus - 2 (10804)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
8OHJ , Knot 72 154 0.78 38 109 147 
GPTPVEEAQQKTIEAITKAINYMAKRRIGALLTIERDTGMGDYIETGIPLNAKVSSELLINIFIPNTPLHDGAVIMKNNEIAAAACYLPLSESPFISKELGTRHRAAVGISEVTDSLTIIVSEETGGVSVAKNGDLHRELTEEALKEMLEAEFK
1ZPL , Knot 82 177 0.80 40 129 168 
AVSFIGSTENDVGPSLGSYSRTHAMDNLPFVYDTRNKIGYQNANVWHISKGFCVGLDGKVDLPVVGSLDGQSIYGLTEEVGLLIWMGDTKYSRGTAMSGNSWENVFSGWCVGANTASTQGLSVRVTPVILKRNSSARYSVQKTSIGSIRMRPYNGSSAGSVQTTVNFSLNPFTLNDT
7JSI , Knot 219 536 0.85 40 266 507 
MPGFYEIVIKVPSDLDGHLPGISDSFVNWVAEKEWELPPDSDMDLNLIEQAPLTVAEKLQRDFLTEWRRVSKAPEALFFVQFEKGESYFHMHVLVETTGVKSMVLGRFLSQIREKLIQRIYRGIEPTLPNWFAVTKTRNGAGGGNKVVDECYIPNYLLPKTQPELQWAWTNMEQYLSACLNLTERKRLVAQHLTHVSQTQEQNKENQNPNSDAPVIRSKTSARYMELVGWLVDKGITSEKQWIQEDQASYISFNAASNSRSQIKAALDNAGKIMSLTKTAPDYLVGQQPVEDISSNRIYKILELNGYDPQYAASVFLGWATKKFGKRNTIWLFGPATTGKTNIAEAIAHTVPFYGCVNWTNENFPFNDCVDKMVIWWEEGKMTAKVVESAKAILGGSKVRVDQKCKSSAQIDPTPVIVTSNTNMCAVIDGNSTTFEHQQPLQDRMFKFELTRRLDHDFGKVTKQEVKDFFRWAKDHVVEVEHEFYVKKGGAKKRPAPSDADISEPKRVRESVAQPSTSDAEASINYADRLARGHSL

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(8OHJ_1)}(2) \setminus P_{f(1ZPL_1)}(2)|=66\), \(|P_{f(1ZPL_1)}(2) \setminus P_{f(8OHJ_1)}(2)|=86\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:1101100100001011001100110001111101000011100100111101010001110111100110011111000011111001110001110001100001111100100010111000011101100101000100011001101010
Pair \(Z_2\) Length of longest common subsequence
8OHJ_1,1ZPL_1 152 4
8OHJ_1,7JSI_1 201 4
1ZPL_1,7JSI_1 203 4

Newick tree

 
[
	7JSI_1:10.05,
	[
		8OHJ_1:76,1ZPL_1:76
	]:32.05
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{331 }{\log_{20} 331}-\frac{154}{\log_{20}154})=53.9\)
Status Protein1 Protein2 d d1/2
Query variables 8OHJ_1 1ZPL_1 69 63
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]